You mentioned only a few of the functions of Mashiach. If someone
only performed those three jobs, it wouldn't be enough to consider
them Mashiach. Cyrus, for instance, would not be able to correct
Torah observance and cause all of Israel to keep Torah completely.
Shoshanna
Cyrus is not just called God's anointed, Cyrus is God's anointed.
That which Cyrus does becomes the job description of any future anointed,
namely to rebuild the temple, rebuild Jerusalem, and to bring home the
exiles.
Cyrus's actions become the prototype.
Best,
Liz Fried